The Relation between the integral and differential form of Amperes Law

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Homework Help Overview

The discussion revolves around the relationship between the integral and differential forms of Ampere's Law in electromagnetism, specifically focusing on deriving the differential form from the integral form while considering the displacement current density.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to derive the differential form of Ampere's law from its integral form but expresses difficulty in achieving useful results. Some participants suggest considering specific integration paths and the limit process to extract the curl of the magnetic field.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the original poster's attempts and offering suggestions for approaching the problem. There is an exchange of questions aimed at understanding the specific challenges faced.

Contextual Notes

The original poster mentions ignoring the displacement current in their initial attempt, which may influence the discussion on how to incorporate it into the differential form of Ampere's law.

Zook104
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The integral form of Ampere's law in vacuum is

∫B\cdotdl=μ_{0}I

(a) Using the relation between I and J, obtain the differential form of Ampere's
law. You may ignore any displacement current.

(b)Define the displacement current density J_{d} in terms of the displacement
field D and show how it modifies the differential form of Ampere's law.

My attempts at this have circular and achieved no useful answers. So all and any help would be greatly appreciated :D
 
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You can consider special paths for the integration - like squares or circles - and then let their size go to zero. The interesting part is how you get rot(B) out of that limit.
 
I am sorry but I don't understand what you mean?
 
Can you be more specific where the problem is?
Alternatively, can you show your previous attempts?
 

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